No zeros occur in this puzzle.

**Across**:

**A**: none of the digits in A across occurs twice in A across.

**G**: F' across / T down.

**H**: the reverse of F down

**J**: this prime number has the same digit sum as U down.

**K**: all digits of K across are different and a multiple of 3. Also, K across equals P down multiplied with the digit sum of N across.

**M**: M across equals J across - 1, and the reverse of M across equals U down - 1.

**N**: a palindrome.

**P**: N across multiplied with the digit sum of Q across.

**Q**: this palindrome and prime number is a divisor of A down.

**R**: a prime number whose reverse is also a prime number.

**S**: a square number.

**V**: a palindrome and prime number.

**X**: a prime number.

**Y**: this palindrome equals N across multiplied with the square root of U down.

**A'**: Z down divided by the digit product of A' across is a square number.

**B'**: this square number has the same digit sum as W down.

**D'**: a prime number.

**F'**: F' across equals the sum of G down and A across, and F' across is a multiple of T down.

**Down**:

**A**: a palindrome and cubic number.

**B**: a prime number.

**C**: P across multiplied with the digit sum of N across.

**D**: a palindrome and prime number.

**E**: the reverse of M across.

**F**: twice I down divided by D' across. Also, the digit sum of F down equals the reverse of R across.

**G**: this square number equals S across multiplied with B' across.

**I**: I down has the same digit sum as F' across.

**L**: the reverse of L down is prime, and L down equals the digit product of A' across.

**O**: the digit product of O down is a square number.

**P**: R across multiplied with the digit sum of N across.

**T**: T down divided by X across equals the reverse of U down.

**U**: a square number.

**W**: W down divided by O down equals A' across.

**Y**: every digit except the first one equals the previous digit plus one.

**Z**: Z down equals 2 to the power of the digit sum of S across.

**C'**: a prime number.

**E'**: this prime number is a divisor of I down.